R: Draw from the distribution of an Exponential Family Random...

simulate.ergm {ergm}

R Documentation

Draw from the distribution of an Exponential Family Random Graph Model

Description

simulate is used to draw from exponential family random network models in their natural parameterizations. See ergm for more information on these models.

Usage

## S3 method for class 'formula'
simulate(object, nsim=1, seed=NULL, theta0,
                          burnin=1000, interval=1000,
                          basis=NULL,
                          statsonly=FALSE,
                          sequential=TRUE,
                          constraints = ~.,
                          control = control.simulate.formula(),
                          verbose=FALSE, ...)
## S3 method for class 'ergm'
simulate(object, nsim=1, seed=NULL, theta0=object$coef,
                       burnin=1000, interval=1000, 
                       statsonly=FALSE,
                       sequential=TRUE,
                       constraints = NULL,
                       control = control.simulate.ergm(),
                       verbose=FALSE, ...)

Arguments

`object`	an R object. Either a `formula` or an `ergm` object. The `formula` should be of the form `y ~ <model terms>`, where `y` is a network object or a matrix that can be coerced to a `network` object. For the details on the possible `<model terms>`, see `ergm-terms`. To create a `network` object in R, use the `network()` function, then add nodal attributes to it using the `%v%` operator if necessary.
`nsim`	Number of networks to be randomly drawn from the given distribution on the set of all networks, returned by the Metropolis-Hastings algorithm.
`seed`	Random number integer seed. The default is `sample(10000000, size=1)`.
`theta0`	Vector of parameters for the model from which the sample is to be drawn. If `object` is of class `ergm`, the default value is the vector of estimated coefficients.
`burnin`	The number of proposals before any MCMC sampling is done. If NULL in simulate.ergm, the value of object$burnin is used.
`interval`	The number of proposals between sampled statistics. If NULL in simulate.ergm, the value of object$interval is used. The program prints a warning if too few proposals are being accepted (if the number of proposals between sampled observations ever equals an integral multiple of 100(1+the number of proposals accepted)).
`basis`	An optional `network` object to start the MCMC algorithm from. This overrides the left-hand-side of the `formula`. If neither a left-hand-side nor a `basis` is present, an error results because the characteristics of the network (e.g., size and directedness) must be specified.
`constraints`	A one-sided formula specifying one or more constraints on the support of the distribution of the networks being simulated. See the documentation for a similar argument for `ergm` for more information. For `simulate.formula`, defaults to no constraints. For `simulate.ergm`, defaults to using the same constraints as those with which `object` was fitted.
`control`	A list of control parameters for algorithm tuning. Constructed using `control.simulate.ergm` or `control.simulate.formula`, which have different defaults.

`statsonly`	If TRUE, return only the network statistics (not the network(s) themselves)
`sequential`	If FALSE, each new simulation (of `nsim`) is always started at the initial network. If TRUE, the end of one simulation is used as the start of the next. Irrelevant when `nsim=1`.

`verbose`	If this is `TRUE`, we will print out more information as we run the program, including (currently) some goodness of fit statistics.
`...`	further arguments passed to or used by methods.

Details

A sample of networks is randomly drawn from the specified model. The model is specified by the first argument of the function. If the first argument is a formula then this defines the model. If the first argument is the output of a call to ergm then the model used for that call is the one fit - and unless theta0 is specified, the sample is from the MLE of the parameters. If neither of those are given as the first argument then a Bernoulli network is generated with the probability of ties defined by prob or theta0.

Note that the first network is sampled after burnin + interval steps, and any subsequent networks are sampled each interval steps after the first.

More information can be found by looking at the documentation of ergm.

Value

If nsim==1, simulate.ergm returns an object of class network. If nsim>1, it returns an object of class network.series that is a list with the following elements:

`formula`	The `formula` used to generate the sample.
`networks`	A list of the generated networks.
`stats`	The n\times p matrix of network change statistics, where n is the sample size and p is the number of network change statistics specified in the model.

Examples

#
# Let's draw from a Bernoulli model with 16 nodes
# and density 0.5 (i.e., theta0 = c(0,0))
#
g.sim <- simulate(network(16) ~ edges + mutual)
#
# What are the statistics like?
#
summary(g.sim ~ edges + mutual)
#
# Now simulate a network with higher mutuality
#
g.sim <- simulate(network(16) ~ edges + mutual, theta0=c(0,2))
#
# How do the statistics like?
#
summary(g.sim ~ edges + mutual)
#
# Let's draw from a Bernoulli model with 16 nodes
# and tie probability 0.1
#
g.use <- network(16,density=0.1,directed=FALSE)
#
# Starting from this network let's draw 5 realizations
# of a edges and 2-star network
#
g.sim <- simulate(~edges+kstar(2),nsim=5,theta0=c(-1.8,0.03),
               basis=g.use,
               burnin=100000,interval=1000)
g.sim
#
# attach the Florentine Marriage data
#
data(florentine)
#
# fit an edges and 2-star model using the ergm function
#
gest <- ergm(flomarriage ~ edges + kstar(2))
summary(gest)
#
# Draw from the fitted model
#
g.sim <- simulate(gest,nsim=100,burnin=1000,interval=1000)
g.sim

[Package ergm version 2.4-3 Index]